Finite Time Conytol For A Class Of Nonlinear Systems

Compared with the asymptotical stability or exponential stability in the sense of traditional Lyapunov,finite time stability has better transient performance and robustness.In recent years,the problem of finite time control has attracted much attention.Finite time control means that the state trajectory of the system can be maintained into a predetermined region within a finite time interval.To achieve control performance within a finite time,terminal sliding mode control(TSMC)is proposed and widely used in a variety of first or second-order systems.Although a few non-singular terminal sliding mode control methods are obtained for the high order system,these results are limited to integral cascade high order nonlinear systems.According to the above analysis,there are still some key problems to be further studied by finite time control,especially for the non-integral high-order uncertain nonlinear systems.In this thesis,we study finite time control problem for a class of non-integral high-order nonlinear systems,namely finite time stabilization problem and finite time tracking control problem.The main contents are as follows:(1)The problem of finite time stabilization for a class of nonlinear systems is studied.A novel distributed sliding mode surface function is proposed for the first time.On the proposed sliding surface function,the characteristic of finite time convergence is ensured.In order to avoid the computational complexity in the backstepping method and the singularity in the higher-order sliding mode control,an improved first order filter based on DSC technology is proposed.The distributed fast stabilizer is finally designed by using backstepping technique,which solves the finite time stabilization problem of the non-integral high-order nonlinear systems.(2)The problem of finite time precise tracking control for a class of uncertain nonlinear systems is studied.Compared with the existing results,uncertain functions are taken into consideration,which greatly increases the difficulty of the design.Under the condition that the structure of the system is relaxed,a distributed fast and precise tracking controller is proposed,which provides a feasible scheme for solving the problem of finite time precise tracking control of uncertain nonlinear systems.The stability analysis and simulation results verify the effectiveness and advantage of the proposed method.